Physical Determinants of Attenuation, Phase and Group Velocity

Physical Determinants of Attenuation, Phase and Group Velocity 

The simplest, but not necessarily complete, description of a propagating wave is to be found in the one-dimensional wave equation, which is in essence a form of Newton s second law Force = Mass x Acceleration, 

Using classical algebra (Bhatia, 1967, Matheson, 1971 McSkimin, 1964), phase velocity is given by  

Three groups of phenomena affect the frequency-dependence of ultrasonic wave propagation classical processes, relaxation, and scattering, of which scattering is likely to dominate in foodstuffs due to their particulate nature. The two classical thermal processes are radiation and conduction of heat away from regions of the material, which are locally compressed due to the passage of a wave they can lead to attenuation but the effect is negligible in liquid materials (Herzfield and Litovitz, 1959 Bhatia, 1967). The third classical process is due to shear and bulk viscosity effects. Attenuation in water approximates to a dependence on the square of the frequency and because of this it is common to express the attenuation in more complex liquids as a( x )/o or a(f)jf2 in order to detect, or differentiate from, water-like properties. 

Relaxation processes occur when a wave propagates through a medium in which there exists any type of equilibrium, which is capable of being disturbed by the material state fluctuations associated with the passage of the wave. Detailed discussion of relaxation phenomena are to be found in 

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